Group #30748751 — subgroups

Subgroups — #30748751

Order 17152.

486 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22560201	C₂	1	2	yes	maximal
2	#22558965	C₂	1	2	yes	maximal, complemented
3	#22558084	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
5	#16863420	C₂²	1	4	yes	—
6	C₂×#14523960	—	2	2	no	—
7	#16863165	—	2	2	no	—
8	#16863147	—	2	2	no	—
9	#16863147	—	2	2	no	—
10	C₂³×C₈×C₆₇	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
12	C₈×D₄×C₆₇	—	2	2	no	—
13	C₈×D₄×C₆₇	—	2	2	no	—
14	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₈×C₆₇	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#11761612	—	2	4	no	—
18	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
19	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
20	#14523960	—	4	4	no	—
21	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₆₇	—	2	2	no	—
24	C₂²×C₈×C₆₇	—	2	2	no	—
25	C₂²×C₈×C₆₇	—	4	4	no	—
26	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
29	C₄×D₄×C₆₇	—	2	2	no	—
30	C₄×D₄×C₆₇	—	2	2	no	—
31	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₆₇	Q₈	1	2	yes	—
33	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
34	C₄⋊C₈×C₆₇	—	2	2	no	—
35	C₂²⋊C₈×C₆₇	—	2	4	no	—
36	C₄×C₈×C₆₇	D₄	1	2	yes	—
37	C₄×C₈×C₆₇	D₄	1	2	yes	—
38	#11761612	—	4	4	no	—
39	#11761612	—	4	4	no	—
40	C₂×C₆₇⋊C₈	—	4	4	no	—
41	C₂⁴×C₆₇	C₄⋊C₄	1	2	yes	—
42	C₂×D₄×C₆₇	—	2	2	no	—
43	C₂×D₄×C₆₇	—	2	2	no	—
44	C₂×D₄×C₆₇	SD₁₆	1	4	yes	—
45	C₂²×C₄×C₆₇	—	2	2	no	—
46	C₂²×C₄×C₆₇	—	2	2	no	—
47	C₂²×C₄×C₆₇	—	4	2	no	—
48	C₂²×C₄×C₆₇	—	4	2	no	—
49	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₆₇	—	2	2	no	—
54	C₂×C₈×C₆₇	—	2	2	no	—
55	C₂×C₈×C₆₇	—	4	1	no	—
56	C₂×C₈×C₆₇	—	4	4	no	—
57	C₂×C₈×C₆₇	—	4	4	no	—
58	C₂×C₈×C₆₇	—	4	2	no	—
59	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₄⋊C₄×C₆₇	—	2	2	no	—
63	C₂²⋊C₄×C₆₇	—	2	4	no	—
64	C₄²×C₆₇	C₂×D₄	1	2	yes	—
65	C₄²×C₆₇	#41	1	2	yes	—
66	C₂³×C₆₇	—	2	2	no	—
67	C₂³×C₆₇	—	2	2	no	—
68	C₂³×C₆₇	—	4	2	no	—
69	C₂³×C₆₇	—	4	2	no	—
70	C₂³×C₆₇	#106	1	4	yes	—
71	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
72	D₄×C₆₇	—	2	8	no	—
73	C₂×C₄×C₆₇	—	2	1	no	—
74	C₂×C₄×C₆₇	—	2	1	no	—
75	C₂×C₄×C₆₇	—	2	2	no	—
76	C₂×C₄×C₆₇	—	4	1	no	—
77	C₂×C₄×C₆₇	—	4	4	no	—
78	C₂×C₄×C₆₇	—	4	2	no	—
79	C₂×C₄×C₆₇	—	4	2	no	—
80	C₂×C₄×C₆₇	—	4	2	no	—
81	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
83	C₂×C₄×C₆₇	#121	1	2	yes	—
84	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
86	C₂×C₄×C₆₇	#135	1	2	yes	—
87	C₈×C₆₇	—	2	1	no	—
88	C₈×C₆₇	—	2	2	no	—
89	C₈×C₆₇	—	4	2	no	—
90	C₈×C₆₇	#100	1	2	yes	complemented
91	C₆₇⋊C₈	—	8	4	no	—
92	C₂²×C₆₇	—	2	1	no	—
93	C₂²×C₆₇	—	2	1	no	—
94	C₂²×C₆₇	—	2	4	no	—
95	C₂²×C₆₇	—	4	4	no	—
96	C₂²×C₆₇	—	4	4	no	—
97	C₂²×C₆₇	—	4	2	no	—
98	C₂²×C₆₇	—	4	2	no	—
99	C₂²×C₆₇	#380	1	1	yes	characteristic
100	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
101	C₂²×C₆₇	#427	1	1	yes	characteristic
102	C₄×C₆₇	—	2	1	no	—
103	C₄×C₆₇	—	2	2	no	—
104	C₄×C₆₇	—	4	2	no	—
105	C₄×C₆₇	C₂×#100	1	1	yes	characteristic
106	C₄×C₆₇	#413	1	1	yes	characteristic
107	C₄×C₆₇	#465	1	4	yes	—
108	#8614	—	67	1	no	maximal, Sylow
109	C₂×C₆₇	—	2	1	no	—
110	C₂×C₆₇	—	2	1	no	—
111	C₂×C₆₇	—	4	4	no	—
112	C₂×C₆₇	#1800	1	1	yes	characteristic
113	C₂×C₆₇	#1807	1	1	yes	characteristic
114	C₂×C₆₇	#1813	1	1	yes	characteristic
115	C₂×C₈×D₄	D₆₇	1	1	yes	characteristic
116	#1800	—	67	2	no	—
117	#1566	—	67	2	no	—
118	#1292	—	67	2	no	—
119	C₆₇	#8614	1	1	yes	characteristic, complemented, Sylow
120	C₂³×C₈	Dic₆₇	1	2	yes	—
121	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
122	C₈×D₄	—	2	2	no	—
123	C₈×D₄	—	2	2	no	—
124	#423	—	67	4	no	—
125	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
126	C₂×#100	—	134	2	no	—
127	C₂×C₂²⋊C₈	Dic₆₇	1	2	yes	—
128	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
129	#343	—	134	2	no	—
130	#334	—	134	2	no	—
131	#334	—	134	2	no	—
132	C₂²×D₄	D₂₆₈	1	1	yes	characteristic
133	C₂³×C₄	C₂×Dic₆₇	1	2	yes	—
134	C₂×M₁₆	—	134	4	no	—
135	C₂²×C₈	—	2	2	no	—
136	C₂²×C₈	—	2	2	no	—
137	C₂²×C₈	—	4	4	no	—
138	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
139	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
140	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
141	C₄×D₄	—	2	2	no	—
142	C₄×D₄	—	2	2	no	—
143	C₂×C₄⋊C₄	D₂₆₈	1	1	yes	characteristic
144	C₂×C₂²⋊C₄	Dic₁₃₄	1	2	yes	—
145	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	134	4	no	—
148	C₄⋊C₈	—	134	4	no	—
149	#100	—	268	4	no	—
150	C₂²⋊C₈	—	2	4	no	—
151	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
152	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
153	C₂⁴	C₄⋊Dic₆₇	1	2	yes	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	2	no	—
156	C₂×D₄	#11761617	1	4	yes	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	—	4	2	no	—
161	C₂²×C₄	C₄⋊Dic₆₇	1	2	yes	—
162	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
163	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
164	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
165	M₁₆	—	268	4	no	—
166	M₁₆	—	268	4	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	4	1	no	—
170	C₂×C₈	—	4	4	no	—
171	C₂×C₈	—	4	4	no	—
172	C₂×C₈	—	4	2	no	—
173	C₂×C₈	—	268	4	no	—
174	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
175	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
176	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
177	C₄⋊C₄	—	2	2	no	—
178	C₂²⋊C₄	—	2	4	no	—
179	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
180	C₄²	#11761628	1	2	yes	—
181	C₂³	—	2	2	no	—
182	C₂³	—	2	2	no	—
183	C₂³	—	4	2	no	—
184	C₂³	—	4	2	no	—
185	C₂³	#14523975	1	4	yes	—
186	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
187	D₄	—	2	8	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
197	C₂×C₄	#14524002	1	1	yes	characteristic
198	C₂×C₄	#14524017	1	2	yes	—
199	C₂×C₄	#14524022	1	2	yes	—
200	C₂×C₄	C₂×#11761617	1	2	yes	—
201	C₂×C₄	#14524065	1	2	yes	—
202	C₈	—	2	1	no	—
203	C₈	—	2	2	no	—
204	C₈	—	4	2	no	—
205	C₈	—	536	4	no	—
206	C₈	#14523960	1	2	yes	complemented
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	4	no	—
210	C₂²	—	4	4	no	—
211	C₂²	—	4	4	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	#16863256	1	1	yes	characteristic
215	C₂²	C₂×#14523975	1	1	yes	characteristic
216	C₂²	#16863434	1	1	yes	characteristic
217	C₄	—	2	2	no	—
218	C₄	—	2	1	no	—
219	C₄	—	4	2	no	—
220	C₄	C₂×#14523960	1	1	yes	characteristic
221	C₄	#16863380	1	1	yes	characteristic
222	C₄	#16863625	1	4	yes	—
223	C₂	—	2	1	no	—
224	C₂	—	2	1	no	—
225	C₂	—	4	4	no	—
226	C₂	#22560201	1	1	yes	characteristic
227	C₂	#22560234	1	1	yes	characteristic
228	C₂	#22560259	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22560201

C₂

yes

maximal

#22558965

C₂

yes

maximal, complemented

#22558084

C₂

yes

maximal, complemented

C₂×C₈×D₄×C₆₇

C₂

yes

maximal, characteristic

#16863420

C₂²

yes

—

—

—

—

—

C₂³×C₈×C₆₇

C₄

yes

—

C₂×C₄×D₄×C₆₇

C₂²

yes

characteristic

C₈×D₄×C₆₇

—

C₈×D₄×C₆₇

—

C₂×C₄⋊C₈×C₆₇

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₆₇

C₄

yes

—

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

C₂×#11761612

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

—

#14523960

—

C₂²×D₄×C₆₇

D₄

yes

characteristic

C₂³×C₄×C₆₇

C₂×C₄

yes

—

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₆₇

C₂×C₄

yes

—

C₂²×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×D₄×C₆₇

—

C₄×D₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₆₇

Q₈

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

C₄⋊C₈×C₆₇

—

C₂²⋊C₈×C₆₇

—

C₄×C₈×C₆₇

D₄

yes

—

C₄×C₈×C₆₇

D₄

yes

—

#11761612

—

#11761612

—

C₂×C₆₇⋊C₈

—

C₂⁴×C₆₇

C₄⋊C₄

yes

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

SD₁₆

yes

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₄⋊C₄

yes

—

C₂²×C₄×C₆₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

C₂×D₄

yes

—

C₄²×C₆₇

#41

yes

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

#106

yes

—

C₂³×C₆₇

C₂×C₄⋊C₄

yes

characteristic

D₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂×C₂²⋊C₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

—

C₂×C₄×C₆₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₆₇

C₂×SD₁₆

yes

—

C₂×C₄×C₆₇

#135

yes

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

#100

yes

complemented

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

#380

yes

characteristic

100

C₂²×C₆₇

C₂×#106

yes

characteristic

101

C₂²×C₆₇

#427

yes

characteristic

102

C₄×C₆₇

—

103

C₄×C₆₇

—

104

C₄×C₆₇

—

105

C₄×C₆₇

C₂×#100

yes

characteristic

106

C₄×C₆₇

#413

yes

characteristic

107

C₄×C₆₇

#465

yes

—

108

#8614

—

maximal, Sylow

109

C₂×C₆₇

—

110

C₂×C₆₇

—

111

C₂×C₆₇

—

112

C₂×C₆₇

#1800

yes

characteristic

113

C₂×C₆₇

#1807

yes

characteristic

114

C₂×C₆₇

#1813

yes

characteristic

115

C₂×C₈×D₄

D₆₇

yes

characteristic

116

#1800

—

117

#1566

—

118

#1292

—

119

C₆₇

#8614

yes

characteristic, complemented, Sylow

120

C₂³×C₈

Dic₆₇

yes

—

121

C₂×C₄×D₄

C₂×D₆₇

yes

characteristic

122

C₈×D₄

—

123

C₈×D₄

—

124

#423

—

125

C₂×C₄⋊C₈

C₂×D₆₇

yes

characteristic

126

C₂×#100

—

134

—

127

C₂×C₂²⋊C₈

Dic₆₇

yes

—

128

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

129

#343

—

134

—

130

#334

—

134

—

131

#334

—

134

—

132

C₂²×D₄

D₂₆₈

yes

characteristic

133

C₂³×C₄

C₂×Dic₆₇

yes

—

134

C₂×M₁₆

—

134

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

C₂×Dic₆₇

yes

characteristic

139

C₂²×C₈

C₂×Dic₆₇

yes

—

140

C₂²×C₈

C₂×Dic₆₇

yes

characteristic

141

C₄×D₄

—

142

C₄×D₄

—

143

C₂×C₄⋊C₄

D₂₆₈

yes

characteristic

144

C₂×C₂²⋊C₄

Dic₁₃₄

yes

—

145

C₂×C₄²

C₂²×D₆₇

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

134

—

148

C₄⋊C₈

—

134

—

149

#100

—

268

—

150

C₂²⋊C₈

—

151

C₄×C₈

C₂²⋊D₆₇

yes

—

152

C₄×C₈

C₂²⋊D₆₇

yes

—

153

C₂⁴

C₄⋊Dic₆₇

yes

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

#11761617

yes

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

C₄⋊Dic₆₇

yes

—

162

C₂²×C₄

C₂²×Dic₆₇

yes

characteristic

163

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

164

C₂²×C₄

C₂×Dic₁₃₄

yes

characteristic

165

M₁₆

—

268

—

166

M₁₆

—

268

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

268

—

174

C₂×C₈

C₂²⋊Dic₆₇

yes

—

175

C₂×C₈

C₂²⋊Dic₆₇

yes

characteristic

176

C₂×C₈

C₂²⋊Dic₆₇

yes

characteristic

177

C₄⋊C₄

—

178

C₂²⋊C₄

—

179

C₄²

C₂×C₂²⋊D₆₇

yes

—

180

C₄²

#11761628

yes

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

#14523975

yes

—

186

C₂³

C₂×C₄⋊Dic₆₇

yes

characteristic

187

D₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

C₂×C₂²⋊Dic₆₇

yes

characteristic

197

C₂×C₄

#14524002

yes

characteristic

198

C₂×C₄

#14524017

yes

—

199

C₂×C₄

#14524022

yes

—

200

C₂×C₄

C₂×#11761617

yes

—

201

C₂×C₄

#14524065

yes

—

202

C₈

—

203

C₈

—

204

C₈

—

205

C₈

—

536

—

206

C₈

#14523960

yes

complemented

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

#16863256

yes

characteristic

215

C₂²

C₂×#14523975

yes

characteristic

216

C₂²

#16863434

yes

characteristic

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

C₂×#14523960

yes

characteristic

221

C₄

#16863380

yes

characteristic

222

C₄

#16863625

yes

—

223

C₂

—

224

C₂

—

225

C₂

—

226

C₂

#22560201

yes

characteristic

227

C₂

#22560234

yes

characteristic

228

C₂

#22560259

yes

characteristic

	subgroup	G/H
center	C₂²	#16863256
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×C₈×D₄×C₆₇	C₂
socle	C₂²×C₆₇	#380
prime radical	C₂²×D₄×C₆₇	D₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₂×C₈×D₄	D₆₇
hypocenter	C₆₇	#8614
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

subgroup

G/H

center

C₂²

#16863256

commutator

C₂²×C₄×C₆₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₂×C₈×D₄×C₆₇

C₂

socle

C₂²×C₆₇

#380

prime radical

C₂²×D₄×C₆₇

D₄

cosocle

C₂×C₄²×C₆₇

C₂³

hypercenter

C₂×C₈×D₄

D₆₇

hypocenter

C₆₇

#8614

LCS

G ▷ C₂²×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×D₄

N	H ≅ G/N	type
2. #22558965	C₂	semidirect
3. #22558084	C₂	semidirect
90. C₈×C₆₇	#100	semidirect
119. C₆₇	#8614	semidirect
206. C₈	#14523960	semidirect

H ≅ G/N

type

2. #22558965

C₂

semidirect

3. #22558084

C₂

semidirect

90. C₈×C₆₇

#100

semidirect

119. C₆₇

#8614

semidirect

206. C₈

#14523960

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22560201	2
#22558965	2
#22558084	2
C₂×C₈×D₄×C₆₇	2
#8614	67

subgroup

index

C₂×C₈×D₄×C₆₇

Subgroups — #30748751

Conjugacy classes of subgroups

Complements

Maximal subgroups